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Optimal Mass Transport on Euclidean
Spaces

to appear on You are still doing things
that I gave up years ago

"Francesco Maggi's book is a
detailed and extremely well written explanation
of the fascinating theory of
MongeKantorovich optimal mass transfer.
I especially recommend Part IV's discussion of the ‘linear’ cost problem and its subtle mathematical resolution." Lawrence C. Evans, University of California, Berkeley "Over the last three
decades, optimal transport has revolutionized
the mathematical analysis of inequalities, differential equations, dynamical systems, and their applications to physics, economics, and computer science. By exposing the interplay between the discrete and Euclidean settings, Maggi's book makes this development uniquely accessible to advanced undergraduates and mathematical researchers with a minimum of prerequisites. It includes the first textbook accounts of the localization technique known as needle decomposition and its solution to Monge's centuries old cutting and filling problem (1781). This book will be an indispensable tool for advanced undergraduates and mathematical researchers alike." Robert McCann, University of Toronto
